I like your first option the best. Then you can still have fun with your horse if things don't progress very fast. And of course no horse is completely "bombproof" and I bet you can find something he is scared of or needs work on and then work on that to improve it. Trust me that is a great way to learn to train.
Just start over with the basics on an already broken horse and just keep going from there. You'll learn a lot and you'll see a lot of improvement and it'll be harder to make crucial mistakes that could be dangerous and would take a lot of work to correct completely.
That's just my advice. That's what I did. If I would have started with a horse that wasn't completely finished I wouldn't have as much positive experience now or as much confidence.